SAAC Review

1. SAAC Review Michael Schilmoeller Tuesday February 2, 2011 SAAC

2. Sources of Uncertainty • Fifth Power Plan • Load requirements • Gas price • Hydrogeneration • Electricity price • Forced outage rates • Aluminum price • Carbon allowance cost • Production tax credits • Renewable Energy Credit (Green tag value) • Sixth Power Plan • aluminum price and aluminum smelter loads were removed • Power plant construction costs • Technology availability • Conservation costs and performance Scope of uncertainty

3. Reduce size and likelihood of bad outcomes Cost – risk tradeoff: reducing risk is a money-losing proposition Imperfect Information No "do-overs", irreversibility ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔ Characteristics Buying an automobile? Resource Planning?

4. Use of scenarios Resource allocations reflect likelihood of scenarios Resource allocations reflect severity of scenarios … even if "we cannot assign probabilities" Some resources in reserve, used only if necessary ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔ Characteristics Buying an automobile? Resource Planning?

5. Identifying Long-Term Ratepayer Needs • Why and for whom is a plant built? • For the market or the ratepayer? • Built for independent power producers (IPPs) for sales into the market, with economic benefits to shareholders? • How much of the plant is attributable to the ratepayer? • This is usually a capacity requirement consideration • To what extent does risk bear on the size of the plant’s share ?

6. How the NWPCCApproach Differs No perfect foresight, use of decision criteria for capacity additions Likelihood analysis of large sources of risk (“scenario analysis”) Adaptive plans that respond to futures

7. Excel Spinner Graph Model Represents one plan responding under each of 750 futures Illustrates “scenario analysis on steroids”

8. The portfolio model $ Modeling Process

9. Space of feasible solutions Efficient Frontier Finding Robust Plans Reliance on the likeliest outcome Risk Aversion

10. Impact on NPV Costs and Risk C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\L813 NPV Costs.xlsm Scope of uncertainty

11. Decision Trees • Estimating the number of branches • Assume possible 3 values (high, medium, low) for each of 9 variables, 80 periods, with two subperiods each; plus 70 possible hydro years, one for each of 20 years, on- and off-peak energy determined by hydro year • Number of estimates cases, assuming independence: 6,048,000 • Studies, given equal number k of possible values for n uncertainties: • Impact of adding an uncertainty: Decision trees & Monte Carlo simulation

12. Monte Carlo Simulation • MC represents the more likely values • The number of samples is determined by the accuracy requirement for the statistics of interest • The number of samples mk necessary to obtain a given level of precision in estimates of averages grows much more slowly than the number of variables k: Decision trees & Monte Carlo simulation

13. Monte Carlo Samples • How many samples are necessary to achieve reasonable cost and risk estimates? • How precise is the sample mean of the tail, that is, TailVaR90? Implication to Number of Futures

14. Assumed Distribution C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\L813 NPV Costs 02.xlsm Implication to Number of Futures

15. Dependence of Tail Average on Sample Size C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\L813 NPV Costs 02.xlsm, worksheet “Samples_75” σ=1.677 Implication to Number of Futures

16. Accuracy and Sample Size • Estimated accuracy of TailVaR90 statistic is still only ± $3.3 B (2σ)!* • *Stay tuned to see why the precision is actually 1000x better than this! Implication to Number of Futures

17. Accuracy Relative to the Efficient Frontier C:\Backups\Plan 6\Studies\L813\Analysis of Optimization Run_L813vL811.xls Implication to Number of Futures

18. Conclusion • At least 75 samples are needed for determining the value of our risk metric • Known distribution of statistic • The precision of the sample • Our risk metric is 1/10 of the total number of futures • We need to test our plan under 750 futures to obtain defensible results Implication to Number of Futures

19. Finding the Best Plan • Each plan is exposed to exactly the same set of futures, except for electricity price • Look for the plan that minimizes cost and risk • Challenge: there may be many plans (Sixth Plan possible resource portfolios:1.3 x 1031) Implication to Number of Plans

20. Space of feasible solutions Efficient Frontier The Set of Plans Precedes the Efficient Frontier Reliance on the likeliest outcome Risk Aversion Implication to Number of Plans

21. Finding the “Best” Plan C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\Asymptotic reduction in risk with increasing plans.xlsm Implication to Number of Plans

22. How Many 20-Year Studies? • How long would this take on the Council’s Aurora2 server? Implication to Computational Burden

23. On the World’s Fastest Machine • Assume a benchmark machine can process 20-year studies as fast: • Xeon 5365, 3.0 MHz, L2 Cache 2x4, 4 cores/4 threads per core • 38 GFLOPS on the LinPack standard • To the extent this machine underperforms the Council server, the time estimate would be longer • Total time requirement for one study on the Tianhe-1A: 3.54 days (3 days, 12 hours, 51 minutes) and estimated cost $37,318 Implication to Computational Burden

24. How Do We AchieveOur Objectives? • If it takes more that a workday to perform the simulation, the risk of making errors begins to dampen exploration • In the next presentation, we consider alternatives and the RPM solution Implication to Computational Burden

25. End